Multilocation Plant Sizing and Timing

In this paper we solve a dynamic multilocation problem. Time is continuous, and demands can grow at varying rates in different markets and at different times. There are economies of scale in building plant capacity. To solve such a problem conditional on a prescribed sequence, we show how to use recent insights into the transportation problem to develop constructive algorithms that are computationally viable and attractive even for large problems. With plant sizes held constant, transportation cost is optimized through continuous time so as to set plant timings. We then treat the plant sizes (and some timings) as continuous variables in a feasible directions procedure to move towards a local optimum.